Properties

Label 18496i
Number of curves $4$
Conductor $18496$
CM -4
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("18496.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18496i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.j4 18496i1 [0, 0, 0, 289, 0] [2] 5120 \(\Gamma_0(N)\)-optimal
18496.j3 18496i2 [0, 0, 0, -1156, 0] [2, 2] 10240  
18496.j1 18496i3 [0, 0, 0, -12716, -550256] [2] 20480  
18496.j2 18496i4 [0, 0, 0, -12716, 550256] [2] 20480  

Rank

sage: E.rank()
 

The elliptic curves in class 18496i have rank \(2\).

Modular form 18496.2.a.j

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - 3q^{9} - 6q^{13} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.